Bhaskar wanted to send some documents to Shakuntala. He had her address…
2024
Bhaskar wanted to send some documents to Shakuntala. He had her address without the 6-digit pin code. He didn’t want to risk sending documents without Pincode. So, he called Shakuntala. She did not give the pin code directly, she said, “The first four digits are 1910 in hexadecimal and the last four digits are 3177 in octal”. Bhaskar could courier the documents now. What is her pin code?
- A.
641663
- B.
641641
- C.
640663
- D.
641666
Attempted by 15 students.
Show answer & explanation
Correct answer: A
Concept: to convert a number written in base b to decimal, multiply each digit by the place-value power of b (counting powers from 0 at the rightmost digit) and add the results — for digits dn ... d1 d0 in base b, the decimal value is dn×bn + ... + d1×b1 + d0×b0.
Convert the first four digits, 1910 (hexadecimal, base 16), to decimal using place values 163, 162, 161, 160: 1×163 + 9×162 + 1×161 + 0×160 = 4096 + 2304 + 16 + 0 = 6416.
Convert the last four digits, 3177 (octal, base 8), to decimal using place values 83, 82, 81, 80: 3×83 + 1×82 + 7×81 + 7×80 = 1536 + 64 + 56 + 7 = 1663.
Compare the two four-digit results, 6416 and 1663: the trailing two digits of the first result (“16”) are identical to the leading two digits of the second result (“16”), so the two numbers share a two-digit overlap.
Merge the two results at the shared overlap: keep 6416 in full and append only the non-overlapping remainder of the second result, “63”, giving the six-digit pin code 641663.
Cross-check: splitting 641663 back into its first four digits (6416) and last four digits (1663) reproduces exactly the two decimal values computed above from 1910 (hex) and 3177 (octal), confirming the merge is consistent.
So Shakuntala’s pin code is 641663.